Graph Theoretic Relationship Modelling
by DschingisKhan
Summary: For the complete graph μ : { Nozomi, Rin, Maki, Honoka, Eli, Hanayo, Umi, Kotori, Nico }, enumerate all non-isomorphic complete subgraphs of rank 3 (3-cliques) with at least single-order frequency deviation from local maxima. Show your work.
1. (Nozomi,Maki,Honoka) intersect the Couch

#AN: Sometimes, usually on the cusp of sleep, I'll get an idea in my head that I can't help writing down. Despite the unbelievably nerdy title and summary, expect this to be sporadically-updated (probably) pure fluff about less-common trios. It will not include Aqours because I don't know them. If and when that statement is invalidated, the formation of nodes may or may not remain disjoint, at my discretion.

* * *

A touch.

A sigh.

A gentle caress.

A poke in that one spot that-

"Oy. Are you trying to start something?"

"Start something? Hmm..." Nozomi pretended to consider for a moment. "Well, Maki-Chan, I could ask you the same thing, no? After all, you're the one on top of me." Ah, there it was, the perfect blush. _Point for me!_

"Ah! Bwuh! Nozomiiii!" she whined, but did not deny. After all, Nozomi really was underneath her, her head partially buried in Nozomi's ample bosom, her arms wrapped around the older girl. "Besides, Honoka is the one on top of both of us."

And she wasn't kidding. Honoka had been sitting on the far end of the couch researching new venues on her mobile when she had rather unceremoniously fallen asleep, phone falling from her hand to get lost in the cushions as she slumped over pinning her companions in place.

"The way she's using your perfect ass as a pillow, I wonder if she planned it this way?" Nozomi taunted, bringing the furiously blushing Maki closer to an emulation of her favourite food. "But if she did, I don't mind so much, being so close to our Maki-tan like this," she added tenderly, smiling a little as she gently threaded her fingers through Maki's hair. "Truly, we are blessed under The Sun. Say, does her head being there mean it's a total eclipse of the butt?" Maki rolled her eyes.

"Nozomi, your taste in music kind of sucks, doesn't it. And I'm saying this as someone who writes peppy, saccharine pop." Nozomi snorted but said nothing, simply relishing in the feeling of Maki's heart beating in time with her own.

"Hey, Nozomi... why _do_ you invoke 'the cards' so much?"

"Because they're right."

"Eh? Isn't that just because their meanings are generic enough that they can apply to almost anyone?"

"You know, Maki, if our orientation was right, you'd be getting a serious groping for doubting me."

"Why, Nozomi, are you saying we're not gay anymore!?" Maki asked in feigned shock. She shook her head a little to dislodge the thought and nestle a little deeper in Nozomi's chest with a contented sigh.

"Hehe, I remember a time when you couldn't possibly have even considered saying that, much less using it as a joke. You were so cute back then... ah, not that you're not cute now, too! Maki-chan is always cute."

"Ka ki ku ke ko, motherfucker," Maki replied with a devious smirk. Nozomi, caught off guard, started shaking as she giggled for a solid minute, hoping the vibrations wouldn't wake up the overworked Honoka.

"I always knew Nicocchi was a bad influence on our cute little Maki-tan," she wheezed.

"Anyway, back to the question. How can you put so much of your trust in the cards when they're designed to be generic and vague?" At this, Nozomi sighed a little.

"I always thought your card was The Fool, but maybe you're The Hermit instead," she mused. "Maki, can you actually explain why an astral projection of your childhood self led us on a merry chase when we went up to your coastal house to record the video for Music S.T.A.R.T?"

"Huh...?" It took her a few moments to realise what Nozomi was talking about. "Eh!? I thought that was a dream!"

"No, no, that was all very real. I don't know why it happened and I encourage you to consider it yourself, but the point is, while I admire your dedication to study and self-betterment, not everything in this world is explained in books." Her tone caused Maki look up from her place in Nozomi's bosom and their eyes met. _Should I just show her? Show them?_ Maki didn't blink as Nozomi searched for the answer in her gaze. "The cards, huh?" she relented, taking a deep breath, and a moment to be happy that Maki rose and fell with it, that they could be this close, acutely aware that she was risking that happiness by- _S_ _talling. You're stalling and dissembling, Nozomi. Trust the ones you love._ "Say, Maki, let me show you a trick."

"Nozomi..." Maki trailed off, as she produced her well-worn deck.

"Here, take a look at the top card and put it back. You don't have to tell me what it is." It was awkward, and Maki was apparently _really_ comfortable, but she reluctantly managed to liberate one of her hands from underneath her lover and peek at what was probably the nine or ten of swords.

"Now, let's consider one of the others. Nicocchi, perhaps? Yes, she'll be a perfect demonstration. Fixing on the idea of Nico..." Snaking her other hand over so she could do it in full view of her audience, she pulled that same top card and showed it to the now-gaping Maki. "I've always thought The Chariot suited her very well."

"What."

"This has been her card for as long as I've known her. That girl doesn't have any clue when to give up," she related fondly.

"But-"

"The cards are _right_ , Maki," she explained with a little more force than intended, and she winced as Maki flinched. Another deep breath. "Sorry, I'm not angry. Just... I've never really shown this to anyone. I believe in us, in μ's, but even then... I suppose I still have a bit of a scaredy cat nature."

"Nozomi, I'd still love you even if you were a professional charlatan, but this makes me feel... weirded out, but also better."

 _And there she is with this matter-of-fact wisdom._

"I never thought I'd say 'Umi is a bad influence on you', but here we are..."

"Still," she mused, "I thought for sure once I finally got you in the sack I'd have plumbed the depths of how astounding you are and laid all your secrets bare. How silly of me."

"Oh ho? Do you need to try laying me bare and plumbing my depths again? Maybe you missed a spot."

"Pervert."

"It's _your_ tongue." Nozomi was grinning with a mix of mirth and lechery now.

" _That_ is all _your_ fault, you know," Maki grumbled. Then she stiffened suddenly. "Wait. Waiiiiiit. Okay, okay, hold up." She looked... pensive? Worried? "Nozomi, how much of... of all this, all of us... how much did you plan? Instigate?"

"In what way?"

"Was μ's something you intended to happen? Our relationship?"

"Oh dear, you've uncovered my secret plot to fall in love by joining an idol group! But it's too late to stop me now! Mwahaha," she joked before turning serious, lifting Maki's hand to her face for a kiss on each knuckle.

"Maki, there is no such thing as fate." Absently, she twined their fingers together. "My cards don't steal your free will any more than every other divination by every other astrologer in the world. Mine may be much more... targeted... but the principle remains that reading one's fate is to change it. There would be no point otherwise."

"The Observer Effect? Huh, never bet against Einstein, even in mysticism," she mused. "Thanks, Nozomi. I'd hate to think..." Maki's hand escaped her grasp to caress her cheek and she nuzzled into the warmth.

"It's fine, my dear, it is wise to be wary even when you know there are higher forces at work."

 _So mercurial! Our Maki is growing too, I suppose._

"You know what, I'd like to do a full reading for you, Maki."

"Oh, oh, me too!"

"Honoka!"

"Yuuuuup!"

"How long were you listening?"

"Ehehe, around the time Nozomi said, 'Maki-chan is always cute!'" She had rolled herself half over so she could hug both of her girls, happily resting her chin in the small of Maki's back. "Nozomi, you're so amazing! I love it! I love you!" Nozomi looked over Maki to meet Honoka's eyes that were incapable of guile and felt a metaphorical weight lift from her soul. The unbridled joy at discovering something new was one of the things that made Honoka so irresistible.

"Oh no," Maki's voice carried a note of long suffering, "so you heard everything. Including the part where I..."

"Ka ki ku ke ko, motherfucker!" she chorused with Honoka, falling back into a renewed giggling fit as Maki groaned and buried her face in her boobs, blushing all the way to her ears.

"You guys!" she whined. "That's not fair!"

"Maki-chan is too cute for us to play fair, though!" Honoka pointed out, "So Nozomi and I have to work together."

"Hmph! Teasing me like that is still unfair."

"Maaaaki," Nozomi, with a husky voice, went for the kill, "be a good sport and we'll work together _later_ , too." Honoka hummed her agreement and Maki shuddered but didn't say anything for while.

"... you mean it?" she asked shyly, her quiet voice still muffled by where she'd buried her face. Nozomi had the clamp down on the urge to squeal and coo and eat her up on the spot. No, that would send the wrong message. Meeting Honoka's eyes, she smiled.

"Everything I am, to you," Nozomi started.

"My Diamond Princess," Honoka finished. They then both took one of Maki's hands and kissed it reverently as she shivered at the conviction in their oath.


	2. (Rin,Kotori,Eli) permute a fitting

#AN: This was kind of a literal fever dream and was largely written in a half-coherent stupor. I've attempted to preserve that ethereal, dreamlike quality while making it somewhat coherent, short though it is.

* * *

(Rin, Kotori, Eli) permute a fitting

Even if she's still somewhat insecure about her own body, Rin loves to see Kotori at work as much as she loves how Eli can manage to make her feel like a normal girl. She honestly enjoys seeing Kotori indulge her passions.

Kotori remarks that a shared passion is coming to model soon. Rin smirks and steals a kiss from Kotori just as Eli walks in.

For some reason, this causes inspiration to strike!

*Flash*

Rin balances on one leg on Kotori's chair, arms spread wide while Eli's measurements are taken. Again. She almost keeps a straight face. They all know it's just an excuse to paw at their Russian beauty: Kotori knows them all by heart. Eli's ability to keep her poise even though she's half-undressed and blushing fiercely is impressive, though.

*Flash*

Eli watches Kotori work intently while Rin balances a pencil on her nose from the floor. Kotori is in one of her working fugue states, the kind where she forgets to blink or eat for long stretches. Rin keeps an ear out for the sounds of an empty stomach.

Sitting on the floor is strategy!

*Flash*

Rin is curled up in a sunny spot, catnapping while Kotori pins the panels for an extravagant floor length blue ball gown. Kotori and Eli freeze when Rin shifts and mewls in contentment. They manage to stifle their giggling enough that her sleep is undisturbed. Barely.

*Flash*

Rin clutches Kotori around the waist from behind, both of them blushing a bit as Eli strikes a seductive pose from the podium. Eli winks and makes a come hither gesture. Cat faced, Rin winks back and pushes Kotori into Eli's arms for a deep kiss.

*Flash*

Rin and Eli stand side-by-side, long practice allowing them synchronise their ridiculous fake oujou laugh while Kotori turns beet red and pushes her fingertips together. They can't keep it up, and dissolve into genuine laughter, leaning on each other to stay upright.

*Flash*

Kotori's face lights up and she hurriedly pushes Rin into the adjoining storage and locks the door. Bemused, Eli waits.

*Flash*

The lock clicks and the door bursts open.

Rin comes barreling out in a perfectly cut pantsuit with tail coat and tiny crown. She nearly knocks Eli over, but manages to sweep her off her feet instead. Eli's mouth forms a little "o" of surprise at the gallantry of the manoeuvre. She's not used to being held like this.

Kotori snaps as many photos as possible.

*Flash*

Kotori nearly busts a gut laughing over Rin's expression, camera abandoned because she's clutching her sides. Rin struggles to remain standing as Eli pouts at the prospect of maybe being "too heavy".

*Flash*

Rin is sitting, still holding Eli in her lap like a bride. Eli loops her hands around Rin's neck and stares lovingly into her eyes. Wide-eyed, Kotori scrambles to retrieve her camera and resume shooting. Her nosebleed coincides with Rin being pulled in for a toe-curling kiss.

*Flash*

Eli is now sitting in Kotori's with chair, singing lightly. At either side, heads resting on her thighs, Kotori and Rin close their eyes to enjoy the tune. Their hands meet over Eli's lap and fingers intertwine.

As she finishes, she looks down, content to bask in the drowsy moment. Reaching out, Eli cards her fingers through their hair.

"I _adore_ you."


	3. (Umi) is reachable by (Nico, Pana)

#AN: And unexpectedly, the remaining three get a scene.

* * *

Umi's head spun as Hanayo and Nico sat on either side of her, nattering incessantly about the events playing out on the TV in her bedroom. She had asked them, the group's foremost experts, for help. Help understanding the daunting and confusing world of idols. But the moment the first of a small tower of DVDs - all with some manner of "limited edition" or "exclusive special" label, natch - got past the copyright screen, they had been talking almost exclusively to each other. Almost as if she wasn't even in the room.

Were she not in the room...

 _Shameless!_ she scolded herself immediately. She knew all too well where _that_ line of thought would have gone. Nowhere proper for polite company, certainly.

Certain because she had been having... those _sorts_ of thoughts... more and more often lately. Shameful ones. Completely unacceptable ones. Not that there was technically anything _wrong_ with Nico writhing in ecstasy as she sat on Umi's f-

She shook her head violently. The thought of Hanayo hungrily descending to the junction between her legs could not be allowed to-

 _I should not... **cannot** disrespect them with such base and disgusting thoughts!_

Biting her cheek to keep some semblance of self control, she squirmed unconsciously as she tried to at least pay attention to the lyrics on the rec-

 _Gods, they're far too suggestive! She's barely older than us! And those dance moves are so ero- arou- **inappropriate!** This is not wholesome!_

Oblivious to her internal struggles, Hanayo and Nico were slowly encroaching on her person. Without a seeming thought, across a span of time she wasn't quite sure of, distracted as she was by not _thinking_ , she realised that Nico's head lay in her lap and Hanayo had captured her right arm and was leaned against her shoulder, their bodies pressed close with the unfamiliar delicate scent that must have been Hanayo's shampoo warning her too late that her position had been overrun.

She was never more glad to have sat in seiza, the better to maintain her flagging composure.

Nico kicked her legs idly, her cute pink polka-dot ankle socks with the lace trim teasing her from the periphery, just begging to be torn away so Umi could suck-

Umi's eyes slammed shut.

 _I am calm. I am tranquil like a still pond._ She attempted to view the situation with a detached distance. She was vaguely surprised to find it was even working, feeling the unbearable lightness of close human contact start to... drift...

"Time, time! Time out!" Nico, of course, called out. The video froze. There was shifting, and a pressure asserted itself on her legs.

Discipline?

"Umi. _You need to breathe._ " Oh. She was hyperventilating. "Come on, breathe with me, Umi. In... and out. In... and out, there's a girl. Stay with me now."

Nico's face... why, it was very close and she closed her eyes to avoid the recrimination in those crimson pools of...

"No, don't stop! Keep breathing, dammit, listen... feel..." A larger hand grabbed her own - Hanayo? - and she allowed it to be lifted and placed... somewhere in front of her. She marveled slightly at the sharp definition of Nico's collarbones, the tiny girl feeling fragile to her calloused fingers. "That's right, feel my breathing. Follow that rhythm. Just like when we dance, stick with it, two sets of ten reps each, don't try to rush it. In... out. In... out... no, no, don't drift out of sync, focus on the breathing, Umi!"

It took a few minutes before the sharpness of consciousness truly reasserted itself. And with it came the feeling of helplessness, of her shame at her own inability to cope with ordinary proximity from her fellow idols. She tore her hand away from Nico's chest as though she'd been burned and hugged herself, shivering at the prospect of them _realising_ what she was thinking and exposing her for the disgusting creature she was.

Nico leaned forward and... surprised her with as big a hug as she could muster.

"Silly thing, if you were uncomfortable you should have just told us." Her tone wasn't sharp but tender and Umi nearly lost herself right then and there.

"I... I wasn't! It's not that at all!" She received a dubious look. "It's... hard to explain. And..." She started at the feeling of Hanayo rubbing circles on her back.

It felt nice.

"Shhh, it's okay, Umi. Nico and I are both here for you no matter what. Take your time."

Under this two-pronged assault, it was an inevitability that she would give in.

Finally, in a very tiny, scared voice, she said simply: "I have... bad thoughts."

The silence was deafening and she chanced looking up to find Nico hadn't recoiled. If anything, she looked... thoughtful.

"I want..." Umi swallowed thickly. This was the moment of truth. "I keep imagining things... l-lewd things. Depraved things." Another shaky breath. "About you. About the others," she whispered. She let the revelation sit. What more was there to say? And somehow, she felt better for having confessed her sins to some of those she had wronged.

Better, not good. The temporary serenity she had found was quickly overtaken by the need to flee.

Well, she tried, at least.

That was when she realised something rather important: Nico was still in her lap, straddling her thighs and preventing her from getting away. Nico's arms were around her neck. Nico's eyes had a dangerously determined glint. _Nico was kissing her full on the lips!_ She started to flail her arms, to try to get away. She failed. They were pinned to her side by Hanayo hugging her from behind.

"Umi!" Nico gently but firmly took hold of her face and forced their eyes to meet. "This. Is. Okay! You're _allowed_ to want this. You're allowed to _enjoy_ this."

She was stunned.

"...R-really?" she mewled pathetically. She wanted to believe, wanted it to be true. Could they be right? Nico's expression softened again and she pulled Umi into another one of those wonderfully warm hugs.

"You're just so tightly wound, you have no idea what's what," she chuckled wistfully. "Of course 'really'. The World's Number One Super Idol said it, after all!"

Umi relaxed slightly, the tension starting to bleed out of her. Hanayo rethreaded her arms to wrap around Umi's belly, warm smooth hands coming their way under her shirt and up, up, _up_ , just shy of brushing the underside of her b-

Her breath hitched as Hanayo nuzzled into her neck and nibbled at her ear. She shuddered, this time not from fear but from the sudden feeling of burning _need_ washing over her.

"It's not fair, Umi. We love you too, you know. Maybe we'll never be first when Honoka and Kotori and Eli exist, but you don't have to push us away. Can we have the opportunity to show you we care?"

"I don't... that is... I..." It would be so easy. To stop running away, to stop fighting those urges. But...

"Easy, don't force it. Take your time and remember we won't judge you." Nico's fingers carded through her hair. "Hanayo's right, you know: we love you no matter what you say. All you have to do is tell us what you want."

Nico and Hanayo's honeyed words stoked the flame within her to an inferno and a small moan escaped her iron control. Nico was taking her lips again as Hanayo sucked on the nape of her neck.

The dam broke.

The dam exploded, really. Her walls came down, and every depraved act and debauched fantasy she'd had since the start of the evening issued forth in lurid detail. Far from running away from the sick individual she revealed herself to be, they repositioned themselves in front of her, each taking a hand and squeezing it in encouragement every time she faltered. By the end, Nico was blushing and grinning. Hanayo's eyes were wide, her mouth parted in a little "o" of fascination. Umi could have sworn she saw a small trail of blood leaking from her nose.

Nico broke the silence.

"Jeeze, Umi, I don't think we'll have time for half that unless we get started _right now!"_

Umi squeaked.


End file.
